Conformational contribution to the heat capacity of the starch and water system

The heat capacities of starch and starch—water have been measured with adiabatic calorimetry and standard differential scanning calorimetry and are reported from 8 to 490 K. The amorphous starch containing 11–26 wt % (53–76 mol %) water shows a partial glass transition decreasing from 372 to 270 K, respectively. Even the dry amorphous starch gradually increases in heat capacity above 270 K beyond that set by the vibrational density of states. This gradual increase in the heat capacity is identified as part of the glass transition of dry starch that is, however, not completed at the decomposition temperature. The heat capacities of the glassy, dry starch are linked to an approximate group vibrational spectrum with 44 degrees of freedom. The Tarasov equation is used to estimate the heat capacity contribution due to skeletal vibrations with the parameters Θ₁ = 795.5 K, Θ₂ = 159 K, and Θ₃ = 58 K for 19 degrees of freedom. The calculated and experimental heat capacities agree better than ±3% between 8 and 250 K. Similarly, the vibrational heat capacity has been estimated for glassy water by being linked to an approximate group vibrational spectrum and the Tarasov equation (Θ₁ = 1105.5 K and Θ₃ = 72.4 K, with 6 degrees of freedom). Below the glass transition, the heat capacity of the solid starch—water system has been estimated from the appropriate sum of its components and also from a direct fitting to skeletal vibrations. Above the glass transition, the differences are interpreted as contributions of different conformational heat capacities from chains of the carbohydrates interacting with water. The conformational parts are estimated from the experimental heat capacities of dry starch and starch—water, decreased by the vibrational and external contributions to the heat capacity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3038–3054, 2001     

Heat capacity of poly(vinyl methyl ether)

The heat capacity of poly(vinyl methyl ether) (PVME) has been measured using adiabatic calorimetry and temperature‐modulated differential scanning calorimetry (TMDSC). The heat capacity of the solid and liquid states of amorphous PVME is reported from 5 to 360 K. The amorphous PVME has a glass transition at 248 K (?25 °C). Below the glass transition, the low‐temperature, experimental heat capacity of solid PVME is linked to the vibrational molecular motion. It can be approximated by a group vibration spectrum and a skeletal vibration spectrum. The skeletal vibrations were described by a general Tarasov equation with three Debye temperatures Θ₁ = 647 K, Θ₂ = Θ₃ = 70 K, and nine skeletal modes. The calculated and experimental heat capacities agree to better than ±1.8% in the temperature range from 5 to 200 K. The experimental heat capacity of the liquid rubbery state of PVME is represented by C_p(liquid) = 72.36 + 0.136 T in J K^?1 mol^?1 and compared to estimated results from contributions of the same constituent groups of other polymers using the Advanced Thermal AnalysiS (ATHAS) Data Bank. The calculated solid and liquid heat capacities serve as baselines for the quantitative thermal analysis of amorphous PVME with different thermal histories. Also, knowing C_p of the solid and liquid, the integral thermodynamic functions of enthalpy, entropy, and free enthalpy of glassy and amorphous PVME are calculated with help of estimated parameters for the crystal. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2141–2153, 2005     

Heat capacity of poly(trimethylene terephthalate)

The heat capacity of poly(trimethylene terephthalate) (PTT) has been measured using adiabatic calorimetry, standard differential scanning calorimetry (DSC), and temperature-modulated differential scanning calorimetry (TMDSC). The heat capacities of the solid and liquid states of semicrystalline PTT are reported from 5 to 570 K. The semicrystalline PTT has a glass transition temperature of 331 K. Between 340 and 480 K, PTT can show exothermic ordering depending on the prior degree of crystallization. The melting endotherm of semicrystalline samples occurs between 480 and 505 K, with a typical onset temperature of 489 K (216°C). The heat of fusion of the semicrystalline samples is about 15 kJ mol⁻¹. For 100% crystalline PTT the heat of fusion is estimated to be 30 ± 2 kJ mol⁻¹. The heat capacity of solid PTT is linked to an approximate group vibrational spectrum and the Tarasov equation is used to estimate the heat capacity contribution due to skeletal vibrations (θ₁ = 550.5 K and θ₂ = θ₃ = 51 K, N_skeletal = 19). The calculated and experimental heat capacities agree to better than ±3% between 5 and 300 K. The experimental heat capacities of liquid PTT can be expressed by: $ C^L_p(exp) $ = 211.6 + 0.434 T J K⁻¹ mol⁻¹ and compare to ±0.5% with estimates from the ATHAS data bank using contributions of other polymers with the same constituent groups. The glass transition temperature of the completely amorphous polymer is estimated to be 310–315 K with a ΔC_p of about 94 J K⁻¹ mol⁻¹. Knowing C_p of the solid, liquid, and the transition parameters, the thermodynamic functions enthalpy, entropy, and Gibbs function were obtained. With these data one can compute for semicrystalline samples crystallinity changes with temperature, mobile amorphous fractions, and resolve the question of rigid-amorphous fractions.© 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2499–2511, 1998     

The thermodynamic properties of polytetrafluoroethylene

Polytetrafluoroethylenes of different crystallinity were analyzed between 220 and 700 K by differential scanning calorimetry. A new computer coupling of the standard DSC is described. The measured heat capacity data were combined with all literature data into a recommended set of thermodynamic properties for the crystalline polymer and a preliminary set for the amorphous polymer (heat capacity, enthalpy, entropy, and Gibbs energy; range 0–700 K). The crystal heat capacities have been linked to the vibrational spectrum with a θ₃ of 54 K, and θ₁ of 250 K, and a full set of group vibrations. C_v to C_p conversion was possible with a Nernst–Lindemann constant of A = 1.6 × 10^?3 mol K/J. The glass transition was identified as a broad transition between 160 and 240 K with a ΔC_p of 9.4 J/K mol. The room-temperature transitions at 292 and 303 K have a combined heat of transition of 850 J/mol and an entropy of transition of 2.90 J/K mol. The equilibrium melting temperature is 605 K with transition enthalpy and entropy of 4.10 kj/mol and 6.78 J/K mol, respectively. The high-temperature crystal from is shown to be a condis crystal (conformationally disordered), and for the samples discussed, the crystallinity model holds.     

The thermal properties of poly(pivalolactone)

Quantitative thermal analysis was carried out for poly-(pivalolactone) (PPVL), including heat capacity determinations from 140 to 550 K. The experimental C_p below the glass transition temperature was fitted to an approximate vibrational spectrum and the ATHAS computation scheme was used to compute the “vibration only” heat capacities from 0.1 to 1000 K. The liquid C_p was derived from an empirical addition scheme and found to agree with the experimental C_p with an RMS of ±2.8% from 240 K to 550 K. A glass transition, T_g, could be detected at 260 K, and the change in heat capacity for 100% amorphous PPVL was calculated to be 38.8 J/(K mol). Above T_g, semicrystalline samples seem to show a rigid amorphous fraction that does not contribute to the increase in heat capacity at T_g. Using the ATHAS recommended heat capacities, the various thermodynamic functions (enthalpy, entropy, and Gibbs function) were derived. The residual entropy at 0 K for the amorphous PPVL was calculated to be 5.2 J/(K mol) per mobile bead, and was comparable to that obtained for a series of linear, aliphatic polyesters analyzed earlier.     

Heat capacity of poly(butylene terephthalate)

The low‐temperature heat capacity of poly(butylene terephthalate) (PBT) was measured from 5 to 330 K. The experimental heat capacity of solid PBT, below the glass transition, was linked to its approximate group and skeletal vibrational spectrum. The 21 skeletal vibrations were estimated with a general Tarasov equation with the parameters Θ₁ = 530 K and Θ₂ = Θ₃ = 55 K. The calculated and experimental heat capacities of solid PBT agreed within better than ±3% between 5 and 200 K. The newly calculated vibrational heat capacity of the solid from this study and the liquid heat capacity from the ATHAS Data Bank were applied as reference values for a quantitative thermal analysis of the apparent heat capacity of semicrystalline PBT between the glass and melting transitions as obtained by differential scanning calorimetry. From these results, the integral thermodynamic functions (enthalpy, entropy, and Gibbs function) of crystalline and amorphous PBT were calculated. Finally, the changes in the crystallinity with the temperature were analyzed. With the crystallinity, a baseline was constructed that separated the thermodynamic heat capacity from cold crystallization, reorganization, annealing, and melting effects contained in the apparent heat capacity. For semicrystalline PBT samples, the mobile‐amorphous and rigid‐amorphous fractions were estimated to complete the thermal analysis. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4401–4411, 2004     

Heat capacities of perfluoropolyethers

The heat capacities at constant pressure of liquid perfluoropolyethers with different chain structures were determined above the glass transition temperature up to 480 K by means of differential scanning calorimetry (DSC). The group contributions of the  O , CF₂ , and  CF(CF₃) were calculated as a function of the temperature. Anomalous behavior of ethereal oxygen in a perfluorinated chain, as previously found for group contributions to the glass transition and to the vaporization energy, was observed also for heat capacity where the oxygen contribution is consistently lower for perfluorinated polyoxides in comparison to the hydrogenated homologous. The jump in c_p at the glass transition follows a regular behavior in the sense that ΔC_p/beadmole is within the average range found by Wunderlich for the majority of polymers. Moreover, data obtained in the present work allow the prediction of c_p of perfluoropolyethers of whatever structure between T_g and 480 K. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2073–2082, 1997     

Reversible and irreversible heat capacity of poly[carbonyl(ethylene‐co‐propylene)] by temperature‐modulated calorimetry

The heat capacity of poly[carbonyl(ethylene‐co‐propylene)] with 95 mol % C₂H₄? CO? (Carilon EP®) was measured with standard differential scanning calorimetry (DSC) and temperature‐modulated DSC (TMDSC). The integral functions of enthalpy, entropy, and free enthalpy were derived. With quasi‐isothermal TMDSC, the apparent reversing heat capacity was determined from 220 to 570 K, including the glass‐ and melting‐transition regions. The vibrational heat capacity of the solid and the heat capacity of the liquid served as baselines for the quantitative analysis. A small amount of apparent reversing latent heat was found in the melting range, just as for other polymers similarly analyzed. With an analysis of the heat‐flow rates in the time domain, information was collected about latent heat contributions due to annealing, melting, and crystallization. The latent heat decreased with time to an even smaller but truly reversible latent heat contribution. The main melting was fully irreversible. All contributions are discussed in the framework of a suggested scheme of six physical contributions to the apparent heat capacity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1565–1577, 2001     

The heat capacity of solid poly(p-xylylene) and polystyrene

The constant-pressure heat capacity C_p of poly(p-xylylene) (PPX) has been measured from 220 to 625 K by differential scanning calorimetry. The constant-volume heat capacities C_v of both, PPX and its isomer polystyrene (PS) have been interpreted in the light of literature data on full normal-mode calculations for PS and estimates from low-molecular-weight analogs for PPX for the 39 group vibrations. Nine skeletal vibrations were used in this discussion with characteristic temperatures θ₁ and θ₃ of 534.5 and 43.1 K for PS. It was also possible to calculate a heat capacity contribution of a phenylene group within a polymer chain. Single 48-vibration θ₁ temperatures of 3230 K for PS and 2960 K for PPX are sufficient to describe C_v above 220 K. Below 140 K, PS heat capacity shows deviations from the Tarasov treatment.     

Physical ageing in poly(vinyl acetate) 1. Enthalpy relaxation

The enthalpy changes ΔH_∞ between a poly(vinyl acetate) glass formed by rapid cooling and the corresponding fully relaxed glass have been estimated at four temperatures below the glass transition. The values obtained were different to those expected by extrapolating liquid behavior below the glass transition and were found to agree well with the predictions of a simple expression for the combined main chain conformational and free volume contributions to enthalpy. Conformational contributions from the side chain alone were also considered but were not required to obtain agreement with experiment. It can be concluded that the side chains remained mobile below the glass transition and do not contribute to the heat capacity discontinuity at T_g. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1107–1116, 1997     

Thermal properties of poly(ester‐imide)s with C12H24 and C22H44 groups

The thermal properties of poly(4,4′‐phthaloimidobenzoyl‐n‐methyleneoxycarbonyl) with n =12 and 22, abbreviated as PEIM‐12 and PEIM‐22, respectively, have been studied using differential scanning calorimetry (DSC). The heat capacities of the solid states of both polymers were measured and compared to computed heat capacities from approximate vibrational spectra. The deviations from the vibrations‐only heat capacity were used to identify large‐amplitude, conformational motions. The heat capacities of the liquid states were described as linear functions of temperature. They agreed with the liquid heat capacities generated from the ATHAS addition scheme using group contributions derived from polymers containing the same chemical segments as the PEIM‐ns. Knowing the heat capacities for the solid and liquid, the transition parameters could be separated and enthalpies, entropies, and free enthalpies obtained. With these data, the change of the crystallinity with temperature could be computed. In the early stages of solidification both compounds contain significant entropy contributions from conformational ordering of the flexible spacer and little from the rigid, aromatic segments. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 319–328, 2000     

Thermal analysis of spider silk inspired di-block copolymers in the glass transition region by TMDSC

We used advanced thermal analysis methods to characterize a new family of A-B di-block copolymers based on the amino acid sequences of Nephila clavipes major ampulate dragline spider silk. Using temperature modulated differential scanning calorimetry with a thermal cycling method and thermogravimetry, we captured the effect of bound water acting as a plasticizer for spider silk-like biopolymer films which had been cast from water solution and then dried. A low glass transition because of bound water removal was observed in the first heating cycle, after which, a shift of glass transition was observed in A-block film due to crystallization and annealing, and in BA film due to annealing. No shift of glass transition after bound water removal was observed in B-block film. The reversing heat capacities, C _p, for temperatures below and above the glass transition were measured and compared to the calculated values. The solid state heat capacity was modeled below T _g, based on the vibrational motions of the constituent poly(amino acid)s, heat capacities of which are known from the ATHAS Data Bank. Excellent agreement was found between the measured and calculated values of the heat capacity, showing that this model can serve as a standard method to predict the solid state C _p for other biologically inspired block-copolymers. We also calculated the liquid state heat capacities of the 100% amorphous biopolymer at T _g, and this predicted value can be use to determined the crystallinity of protein-based materials.     

Crystallization and melting of a branched polyethylene with precisely controlled chemical structure

The heat capacity of a linear polyethylene with dimethyl branches, at every 21st backbone atom was analyzed by differential scanning calorimetry (DSC) and quasi-isothermal temperature-modulated DSC. This novel copolyethylene (PE2M) is relatively difficult to crystallize from the melt. On subsequent heating, a first, sharp melting peak is followed by a sharp cold-crystallization and crystal perfection and a smaller endotherm, before reaching the main melting at 315–320 K, close to the melting temperatures of eicosane and tetracontane. The low-temperature melting is sensitive to the cooling rate and disappears below 1.0 K min⁻¹. The cold crystallization can be avoided by heating with rates faster than 80 K min⁻¹. The PE2M exhibits some reversing and reversible melting, which is typical for chain-folded polymers. The glass transition of semicrystalline PE2M is broadened and reaches its upper limit at about 260 K (midpoint at about 0.355 K). Above this temperature, the crystals seem to have a heat capacity similar to that of the liquid. A hypothesis is that the melting transition can be explained by changes in crystal perfection without major alteration of the crystal structure and the lamellar morphology. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3461–3474, 2006     

Heat capacity of amorphous polyhexene-1 between 20 and 300°K: Intramolecular vibrational contribution to Cv below the glass transition

The heat capacity of polyhexene-1 was measured between 20 and 300°K. The apparatus, an adiabatic calorimeter giving results with a random error of 0.2–0.4%, is briefly described. The characterization of the sample by x-ray diffraction patterns established that it was amorphous at all temperatures. Gold foil was incorporated with the sample to increase the apparent thermal diffusivity and so to decrease the time needed for the measurements. The glass transition temperature was found to be 215.5 ± 1°K. On the C_p curve, no subglass anomaly was detected, unlike the results of experiments described elsewhere. The calculation of C_v is discussed, and an explanation is given for the choice of the number of intramolecular vibrational modes per monomer which are assumed to contribute to C_v. A linear continuum model with characteristic temperature θ₁ = 736°K allows us to fit the experimental curve over a temperature range of 140°K.     

Modulated differential scanning calorimetry

Modulated-temperature differential scanning calorimetry was used to measure the glass transition temperature,T _g, the heat capacity relaxation in the glassy state and the increment of heat capacity, C_p, in the glass transition region for several polymers. The differential of heat capacity with respect to temperature was used to analyseT _g and C_p simply and accurately. These measurements are not affected by complex thermal histories.     

Analysis of a symmetric neopolyol ester

Quantitative thermal analysis was carried out for tetra[methyleneoxycarbonyl(2,4,4-trimethyl)pentyl]methane. The ester has a glass transition temperature of 219 K and a melting temperature of 304 K. The heat of fusion is 51.3 kJ mol^?1, and the increase in heat capacity at the glass transition is 250 J K^?1 mol^?1. The measured and calculated heat capacities of the solid and liquid states from 130 to 420 K are reported and a discussion of the glass and melting transitions is presented. The computation of the heat capacity made use of the Advanced Thermal Analysis System, ATHAS, using an approximate group-vibration spectrum and a Tarasov treatment of the skeletal vibrations. The experimental and calculated heat capacities of the solid ester were compared over the whole temperature range to detect changes in order and the presence of large-amplitude motion. An addition scheme for heat capacities of this and related esters was developed and used for the extrapolation of the heat capacity of the liquid state for this ester. The liquid heat capacity for the title ester is well represented by 691.1+1.668T [J K^?1 mol^?1]. A deficit in the entropy and enthalpy of fusion was observed relative to values estimated from empirical addition schemes, but no gradual disordering was noted outside the transition region. The final interpretation of this deficit of conformational entropy needs structure and mobility analysis by solid state¹³C NMR and X-ray diffraction. These analyses are reported in part II of this investigation.     

Simultaneous kinetic and microdielectric studies of some epoxy–amine systems

Three reactive epoxy–amine systems based on diglycidyl ether of bisphenol A (DGEBA) with 4,4′-diaminodiphenylsulfone (DDS), 4,4′-methylenebis [3-chloro 2,6-diethylaniline] (MCDEA), and 4,4′-methylenebis [2,6-diethylaniline] (MDEA), were studied during isothermal curings at 140 and 160°C. The simultaneous kinetic and dielectric studies allow to express conductivity, σ, in terms of conversion, x, and of glass transition temperature, T_g. The conductivity, σ₀, of the initial monomer mixture and, σ_∞ of the fully cured network are measured. It is found that:

• The glass transition temperature, T_g, versus conversion, x, curves follows the equation of Di Benedetto modified by Pascault and Williams
• There exists a linear relation between log σ/log σ₀ and T_g.

So, it is possible to predict both kinetic and dielectric behaviors of these epoxy-amine systems by the knowledge of T_g0, ΔC_p0, and σ₀, respectively, glass transition temperature, heat capacity, and conductivity of initial monomer mixture, T_g∞ and ΔC_p∞, and σ_∞, respectively, glass transition temperature and heat capacity and conductivity of fully cured network. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2911–2921, 1998     

Phase transitions in mesophase macromolecules. VI. The transitions in poly(oxy-2,2′-dimethylazoxybenzene-4,4′-diyloxydodecanedioyl)

The transitions of poly(oxy-2,2′-dimethylazoxybenzene-4,4′-diyloxydodecanedioyl) (PDAD) have been analyzed by differential scanning calorimetry, optical microscopy, and light scattering. The mesophase glass devitrifies at 288 K [ΔC_p = 220 J/K mol]. Crystallization from the liquid mesophase can be described between 322 and 362 K by an Avrami expression with an exponent between 3 and 4. Results of light scattering and optical microscopy are in accord with a spherulitic morphology grown after athermal nucleation. Melting of the semicrystalline samples (crystallinity up to 58%) occurs at about 391 K. The heat of fusion of the completely crystalline sample is calculated to be only 13.55 kJ/mol. The mesophase to isotropic phase transition occurs at 418 K with a heat of transition of 4.1 kJ/mol. A general discussion of these transitions is given.     

Heat capacity of a polydiacetylene single crystal from 3 to 300 K

Heat capacities C_p of a polydiacetylene-bis(toluene sulfonate) single crystal and its monomer have been measured in the temperature range from 3 to 300 K. The temperature dependence of C_p for both monomer and polymer crystals differs from that for monoatomic solids. By applying a chain lattice model for a polymer crystal, the temperature dependence of the heat capacity can be described assuming a phonon density of states given by bending and stretching modes of the polymer backbone. With a combination of one-dimensional and three-dimensional elastic continuum approximations, the heat capacity has been calculated and a good fit to the data has been obtained. A small peak in C_p was detected at 161 K for the monomer and at 198 K for the polymer. This may be ascribed to a lower-temperature phase transition in the polydiacetylene crystals evidenced by previous x-ray and spectroscopic measurements.     

Behavior of [`(a)] 20 \bar \alpha _2^0 T of aqueous urea near the singularity point

Relations for the apparent molar heat capacity ϕ_c of urea in an aqueous solution depending on the molality m and temperature were obtained. A transition to the relations ϕ_c(m,T) for D₂O-(ND₂)₂CO and T₂O-(NT₂)₂CO systems was effected by temperature scaling. At low temperatures, the isotherms of the molar heat capacity C _p(m) of the protium and deuterium systems have minima shifted to more dilute solutions at elevated temperatures. At m = 1, C _p of a solution does not depend on temperature in both systems. The dependences C _p(T) also have minima at constant concentrations. The temperature of the minimum heat capacity is most effectively lowered by small additions of urea. For m = 0.25, T _min is 7.5 K lower than T _min of pure water, and its heat capacity is 0.08 J/(mol K) higher. A transition from m = 1.5 to m = 2 lowers the temperature of the minimum heat capacity by 3.6 K; thus, the heat capacity of solutions differs by 0.02 J/(mol K) only.